Abstract base class for multivariate orthogonal polynomials. More...

#include <Stokhos_OrthogPolyBasis.hpp>

Inheritance diagram for Stokhos::OrthogPolyBasis< ordinal_type, value_type >:

Public Member Functions
	OrthogPolyBasis ()
	Constructor.

virtual	~OrthogPolyBasis ()
	Destructor.

virtual ordinal_type	order () const =0
	Return order of basis.

virtual ordinal_type	dimension () const =0
	Return dimension of basis.

virtual ordinal_type	size () const =0
	Return total size of basis.

virtual const Teuchos::Array < value_type > &	norm_squared () const =0
	Return array storing norm-squared of each basis polynomial. More...

virtual const value_type &	norm_squared (ordinal_type i) const =0
	Return norm squared of basis polynomial `i`.

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const =0
	Compute triple product tensor. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeLinearTripleProductTensor () const =0
	Compute linear triple product tensor where k = 0,1.

virtual value_type	evaluateZero (ordinal_type i) const =0
	Evaluate basis polynomial `i` at zero.

virtual void	evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const =0
	Evaluate basis polynomials at given point `point`. More...

virtual void	print (std::ostream &os) const =0
	Print basis to stream `os`.

virtual const std::string &	getName () const =0
	Return string name of basis.

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::OrthogPolyBasis< ordinal_type, value_type >

Abstract base class for multivariate orthogonal polynomials.

This class provides an abstract interface for multivariate orthogonal polynomials. Orthogonality is defined by the inner product

$(f,g) = \langle fg \rangle = \int_{R^d} f(x)g(x) \rho(x) dx$

where $\rho$ is the density function of the measure associated with the orthogonal polynomials and $d$ is the dimension of the domain.

Like most classes in Stokhos, the class is templated on the ordinal and value types. Typically ordinal_type = int and value_type = double.

Member Function Documentation

template<typename ordinal_type, typename value_type>

virtual Teuchos::RCP< Stokhos::Sparse3Tensor<ordinal_type, value_type> > Stokhos::OrthogPolyBasis< ordinal_type, value_type >::computeTripleProductTensor ( ) const

pure virtual

Compute triple product tensor.

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j,k=0,\dots,P$ where $P$ is size()-1.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >.

template<typename ordinal_type, typename value_type>

virtual void Stokhos::OrthogPolyBasis< ordinal_type, value_type >::evaluateBases	(	const Teuchos::ArrayView< const value_type > &	point,
		Teuchos::Array< value_type > &	basis_vals
	)		const

pure virtual

Evaluate basis polynomials at given point point.

Size of returned array is given by size(), and coefficients are ordered from order 0 up to size size()-1.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >.

template<typename ordinal_type, typename value_type>

virtual const Teuchos::Array<value_type>& Stokhos::OrthogPolyBasis< ordinal_type, value_type >::norm_squared ( ) const

pure virtual

Return array storing norm-squared of each basis polynomial.

Entry $l$ of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where $P$ is size()-1.

Implemented in Stokhos::CompletePolynomialBasis< ordinal_type, value_type >, Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >, Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >, Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >, Stokhos::TensorProductBasis< ordinal_type, value_type, coeff_compare_type >, Stokhos::TotalOrderBasis< ordinal_type, value_type, coeff_compare_type >, and Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >.

Referenced by Stokhos::QuadraturePseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::QuadraturePseudoSpectralOperator().

The documentation for this class was generated from the following file:

Stokhos_OrthogPolyBasis.hpp

Public Member Functions

Detailed Description

template<typename ordinal_type, typename value_type> class Stokhos::OrthogPolyBasis< ordinal_type, value_type >

Member Function Documentation

template<typename ordinal_type, typename value_type>
class Stokhos::OrthogPolyBasis< ordinal_type, value_type >